Abstract. We study the circuit QED architecture and out-of-equilibrium Quantum Thermodynamics of one and two coupled Superconducting Qubits (SQs). SQs, also called artificial atoms, are circuit elements composed by metal wiring that are cooled down towards millikelvin temperatures, until they become superconducting and acquire quantum properties. In certain regimes of their parameters, only two of their energy levels are important and thus their behavior is that of a two-level system, hence the terms qubit and atom used to describe them. An example of SQ is a system called Cooper Pair Box (CPB). Even more promising are the Transmons, which are the protagonists of this talk. In particular, we demonstrate the entanglement between two Transmons in the dispersive regime, mediated through virtual excitations of a resonator connecting them, and we study the effect work done on one of them could have on the other. The results are pretty surprising: we can control the structure of the stationary states of the two coupled Transmons by opportunely tuning their transition frequencies in the dispersive regime, and a particular value exists of the ratios E_{J}/E_{C} of both of them for which the interaction between them is the strongest. Both of these things are extremely important for the implementation of SQs as hardware for the future Quantum Computer, which is our ultimate goal.